The primary goal of this proposal is to study magnetic forces on electric currents in biological tissue, and to analyze and develop new imaging techniques that use these "magneto-acoustic" effects. In the last two decades, many researchers have proposed magneto-acoustic methods to image current and conductivity, and have suggested that magnetic forces and the resulting displacements may play a role in magnetic resonance imaging. At the moment, experiment is leading theory in this field, and this proposal will provide a broad, unified theoretical framework upon which these experimental methods can be built. The research draws upon a variety of fields, including bioelectricity, biomagnetism, and elasticity. There are five specific aims. Specific Aim 1: Calculate the magnitude and distribution of displacement caused by the Lorentz force (the force on a current in a magnetic field) during magnetic resonance imaging. Displacements caused by the Lorentz force has been proposed as a mechanism to image neural action currents, and this aim will examine if such a mechanism is possible. Specific Aim 2: Determine the effect of anisotropy during magneto-acoustic tomography with magnetic induction. This technique has been proposed as a way to image electrical conductivity, but initial studies considered only isotropic tissue. Anisotropy may play a crucial role in magnetoacoustic tomography. Specific Aim 3: Analyze theoretically the relationship between conductivity gradients and the ultrasonically-induced Lorentz force. The inverse of magneto-acoustic imaging is ultrasonically-induced voltages arising from the Lorentz force. This aim will develop general mathematical techniques to image action currents from nerve and muscle using ultrasound. Specific Aim 4: Develop a mechanical bidomain model to analyze the Lorentz force on cardiac wave fronts. The electrical bidomain model is widely used to represent the electrical properties of cardiac tissue. In this aim, a similar model will be developed for the mechanical properties of tissue, which accounts for the elastic properties of the intracellular space, the extracellular space, and their coupling through the cell membrane. Specific Aim 5: Compute the magnetic field produced by cardiac tissue, and determine its influence during magnetic resonance imaging. Many researchers have sought a way to use magnetic resonance imaging to detect neural action currents. However, the current produced by a nerve is small compared to the current produced by the heart. In this aim, the MRI signature of a cardiac action potential wave front will be calculated. All five of these aims are addressed using theoretical and computational methods, and the results will be compared to existing experimental data.